Usually, a fuel cell system comprises at least one reformer for generating a reformate gas and at least one fuel cell for generating electric current. In the case of high-temperature fuel cells, so-called SOFC-fuel cells, soot deposition on the anode can occur in operation, which over time reduces the efficiency of the anode or of the electrolyte. This is accompanied by a decrease of the efficiency of the fuel cell or of the fuel cell system.